Theoretical Analysis of Subthreshold Oscillatory Behaviors in Nonlinear Autonomous Systems

TL;DR

This paper introduces a linearization method to analyze subthreshold oscillations in nonlinear autonomous systems, accurately predicting oscillatory behaviors and extending the approach to general systems.

Contribution

A novel linearization technique for analyzing subthreshold oscillations in nonlinear autonomous systems, validated with neuronal models and generalized to arbitrary systems.

Findings

Accurately predicts damping coefficients and oscillatory frequencies

Shows good agreement with experimental observations

Generalizes to a wide class of autonomous nonlinear systems

Abstract

We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict quantitatively the subthreshold oscillatory activities, including the damping coefficients and the oscillatory frequencies which are in good agreement with those observed in experiments. Then we generalize the linearization method to an arbitrary autonomous nonlinear system. The detailed extension of this theoretical approach is also presented and further discussed.